Simplify 6/( square root of 2- square root of 3)

$\frac{6}{\sqrt{2} - \sqrt{3}}$

Step 1

Multiply $\frac{6}{\sqrt{2} - \sqrt{3}}$ by $\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} + \sqrt{3}}$ .

$\frac{6}{\sqrt{2} - \sqrt{3}} \cdot \frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} + \sqrt{3}}$

Step 2

Multiply $\frac{6}{\sqrt{2} - \sqrt{3}}$ by $\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} + \sqrt{3}}$ .

$\frac{6 (\sqrt{2} + \sqrt{3})}{(\sqrt{2} - \sqrt{3}) (\sqrt{2} + \sqrt{3})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{6 (\sqrt{2} + \sqrt{3})}{{\sqrt{2}}^{2} + \sqrt{6} - \sqrt{6} - {\sqrt{3}}^{2}}$

Step 4

Simplify.

$\frac{6 (\sqrt{2} + \sqrt{3})}{- 1}$

Step 5

Simplify the expression.

Move the negative one from the denominator of $\frac{6 (\sqrt{2} + \sqrt{3})}{- 1}$ .

$- 1 \cdot (6 (\sqrt{2} + \sqrt{3}))$

Rewrite $- 1 \cdot (6 (\sqrt{2} + \sqrt{3}))$ as $- (6 (\sqrt{2} + \sqrt{3}))$ .

$- (6 (\sqrt{2} + \sqrt{3}))$

Step 6

Apply the distributive property.

$- (6 \sqrt{2} + 6 \sqrt{3})$

Step 7

Apply the distributive property.

$- (6 \sqrt{2}) - (6 \sqrt{3})$

Step 8

Multiply.

Multiply $6$ by $- 1$ .

$- 6 \sqrt{2} - (6 \sqrt{3})$

Multiply $6$ by $- 1$ .

$- 6 \sqrt{2} - 6 \sqrt{3}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- 6 \sqrt{2} - 6 \sqrt{3}$

Decimal Form:

$- 18.87758621 \dots$